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- ItemAnalysis of catalyst surface wetting: The early stage of epitaxial germanium nanowire growth(Frankfurt, M. : Beilstein-Institut zur Förderung der Chemischen Wissenschaften, 2020) Ernst, Owen C.; Lange, Felix; Uebel, David; Teubner, Thomas; Boeck, TorstenThe dewetting process is crucial for several applications in nanotechnology. Even though not all dewetting phenomena are fully understood yet, especially regarding metallic fluids, it is clear that the formation of nanometre-sized particles, droplets, and clusters as well as their movement are strongly linked to their wetting behaviour. For this reason, the thermodynamic stability of thin metal layers (0.1-100 nm) with respect to their free energy is examined here. The decisive factor for the theoretical considerations is the interfacial energy. In order to achieve a better understanding of the interfacial interactions, three different models for estimating the interfacial energy are presented here: (i) fully theoretical, (ii) empirical, and (iii) semi-empirical models. The formation of nanometre-sized gold particles on silicon and silicon oxide substrates is investigated in detail. In addition, the strengths and weaknesses of the three models are elucidated, the different substrates used are compared, and the possibility to further process the obtained particles as nanocatalysts is verified. The importance of a persistent thin communication wetting layer between the particles and its effects on particle size and number is also clarified here. In particular, the intrinsic reduction of the Laplace pressure of the system due to material re-evaporation and Ostwald ripening describes the theoretically predicted and experimentally obtained results. Thus, dewetting phenomena of thin metal layers can be used to manufacture nanostructured devices. From this point of view, the application of gold droplets as catalysts to grow germanium nanowires on different substrates is described. © 2020 Ernst et al.
- ItemRevolutions in energy input and material cycling in Earth history and human history(München : European Geopyhsical Union, 2016) Lenton, Timothy M.; Pichler, Peter-Paul; Weisz, HelgaMajor revolutions in energy capture have occurred in both Earth and human history, with each transition resulting in higher energy input, altered material cycles and major consequences for the internal organization of the respective systems. In Earth history, we identify the origin of anoxygenic photosynthesis, the origin of oxygenic photosynthesis, and land colonization by eukaryotic photosynthesizers as step changes in free energy input to the biosphere. In human history we focus on the Palaeolithic use of fire, the Neolithic revolution to farming, and the Industrial revolution as step changes in free energy input to human societies. In each case we try to quantify the resulting increase in energy input, and discuss the consequences for material cycling and for biological and social organization. For most of human history, energy use by humans was but a tiny fraction of the overall energy input to the biosphere, as would be expected for any heterotrophic species. However, the industrial revolution gave humans the capacity to push energy inputs towards planetary scales and by the end of the 20th century human energy use had reached a magnitude comparable to the biosphere. By distinguishing world regions and income brackets we show the unequal distribution in energy and material use among contemporary humans. Looking ahead, a prospective sustainability revolution will require scaling up new renewable and decarbonized energy technologies and the development of much more efficient material recycling systems – thus creating a more autotrophic social metabolism. Such a transition must also anticipate a level of social organization that can implement the changes in energy input and material cycling without losing the large achievements in standard of living and individual liberation associated with industrial societies.
- ItemWhen Density Functional Approximations Meet Iron Oxides(Washington, DC : Soc., 2016) Meng, Yu; Liu, Xing-Wu; Huo, Chun-Fang; Guo, Wen-Ping; Cao, Dong-Bo; Peng, Qing; Dearden, Albert; Gonze, Xavier; Yang, Yong; Wang, Jianguo; Jiao, Haijun; Li, Yongwang; Wen, Xiao-DongThree density functional approximations (DFAs), PBE, PBE+U, and Heyd-Scuseria-Ernzerhof screened hybrid functional (HSE), were employed to investigate the geometric, electronic, magnetic, and thermodynamic properties of four iron oxides, namely, α-FeOOH, α-Fe2O3, Fe3O4, and FeO. Comparing our calculated results with available experimental data, we found that HSE (a = 0.15) (containing 15% "screened" Hartree-Fock exchange) can provide reliable values of lattice constants, Fe magnetic moments, band gaps, and formation energies of all four iron oxides, while standard HSE (a = 0.25) seriously overestimates the band gaps and formation energies. For PBE+U, a suitable U value can give quite good results for the electronic properties of each iron oxide, but it is challenging to accurately get other properties of the four iron oxides using the same U value. Subsequently, we calculated the Gibbs free energies of transformation reactions among iron oxides using the HSE (a = 0.15) functional and plotted the equilibrium phase diagrams of the iron oxide system under various conditions, which provide reliable theoretical insight into the phase transformations of iron oxides.
- ItemSubstrate-orientation dependence of β -Ga2O3 (100), (010), (001), and (2 ̄ 01) homoepitaxy by indium-mediated metal-exchange catalyzed molecular beam epitaxy (MEXCAT-MBE)(Melville, NY : AIP Publ., 2020) Mazzolini, P.; Falkenstein, A.; Wouters, C.; Schewski, R.; Markurt, T.; Galazka, Z.; Martin, M.; Albrecht, M.; Bierwagen, O.We experimentally demonstrate how In-mediated metal-exchange catalysis (MEXCAT) allows us to widen the deposition window for β-Ga2O3 homoepitaxy to conditions otherwise prohibitive for its growth via molecular beam epitaxy (e.g., substrate temperatures ≥800 °C) on the major substrate orientations, i.e., (010), (001), (2⎯⎯01), and (100) 6°-offcut. The obtained crystalline qualities, surface roughnesses, growth rates, and In-incorporation profiles are shown and compared with different experimental techniques. The growth rates, Γ, for fixed growth conditions are monotonously increasing with the surface free energy of the different orientations with the following order: Γ(010) > Γ(001) > Γ(2⎯⎯01) > Γ(100). Ga2O3 surfaces with higher surface free energy provide stronger bonds to the surface ad-atoms or ad-molecules, resulting in decreasing desorption, i.e., a higher incorporation/growth rate. The structural quality in the case of (2⎯⎯01), however, is compromised by twin domains due to the crystallography of this orientation. Notably, our study highlights β-Ga2O3 layers with high structural quality grown by MEXCAT-MBE not only in the most investigated (010) orientation but also in the (100) and (001) ones. In particular, MEXCAT on the (001) orientation results in both growth rate and structural quality comparable to the ones achievable with (010), and the limited incorporation of In associated with the MEXCAT deposition process does not change the insulating characteristics of unintentionally doped layers. The (001) surface is therefore suggested as a valuable alternative orientation for devices.
- ItemEditors' Choice - Precipitation of Suboxides in Silicon, their Role in Gettering of Copper Impurities and Carrier Recombination(Pennington, NJ : ECS, 2020) Kissinger, G.; Kot, D.; Huber, A.; Kretschmer, R.; Müller, T.; Sattler, A.This paper describes a theoretical investigation of the phase composition of oxide precipitates and the corresponding emission of self-interstitials at the minimum of the free energy and their evolution with increasing number of oxygen atoms in the precipitates. The results can explain the compositional evolution of oxide precipitates and the role of self-interstitials therein. The formation of suboxides at the edges of SiO2 precipitates after reaching a critical size can explain several phenomena like gettering of Cu by segregation to the suboxide region and lifetime reduction by recombination of minority carriers in the suboxide. It provides an alternative explanation, based on minimized free energy, to the theory of strained and unstrained plates. A second emphasis was payed to the evolution of the morphology of oxide precipitates. Based on the comparison with results from scanning transmission electron microscopy the sequence of morphology evolution of oxide precipitates was deduced. It turned out that it is opposite to the sequence assumed until now. © 2020 The Author(s). Published on behalf of The Electrochemical Society by IOP Publishing Limited.
- ItemDimethyl carbonate synthesis from carbon dioxide using ceria–zirconia catalysts prepared using a templating method: characterization, parametric optimization and chemical equilibrium modeling(London : RSC Publishing, 2016) Kumar, Praveen; With, Patrick; Srivastava, Vimal Chandra; Shukla, Kartikeya; Gläser, Roger; Mishra, Indra ManiIn this paper, a series of CexZr1−xO2 solid solution spheres were synthesized by exo- and endo-templating methods and tested for dimethyl carbonate (DMC) synthesis using direct conversion of CO2. The synthesized catalysts were characterized by X-ray diffraction (XRD), N2-physisorption, scanning electron microscopy (SEM), and CO2/NH3-temperature-programmed desorption (TPD). Formation of CexZr1−xO2 solid solutions with tetragonal and cubic crystal structures depending on cerium/zirconium compositions was confirmed by XRD analysis. The specific surface area of the mixed oxide decreased and the average pore diameter increased with an increase in the ceria content, with the exception of the mixed oxides with x = 0.4–0.5 i.e. Ce0.4Zr0.6O2 and Ce0.5Zr0.5O2. The basic and acidic site density of the synthesized catalysts was in the order: ZrO2 < CeO2 < Ce0.5Zr0.5O2, and the basic and acidic site density per unit area followed the same order. The best Ce0.5Zr0.5O2 catalyst was further used for the optimization of reaction conditions such as reaction time, reaction temperature, catalyst dose and reusability for DMC synthesis. Furthermore, study of chemical equilibrium modeling was done using the Peng–Robinson–Stryjek–Vera equation of state (PRSV-EoS) along with the van der Waals one-fluid reaction condition so as to calculate change of Gibbs free energy (ΔG°) and heat of reaction (ΔH°).
- ItemA variational formula for the free energy of an interacting many-particle system(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Adams, Stefan; Collevecchio, Andrea; König, WolfgangWe consider $N$ bosons in a box in $R^d$ with volume $N/rho$ under the influence of a mutually repellent pair potential. The particle density $rhoin(0,infty)$ is kept fixed. Our main result is the identification of the limiting free energy, $f(beta,rho)$, at positive temperature $1/beta$, in terms of an explicit variational formula, for any fixed $rho$ if $beta$ is sufficiently small, and for any fixed $beta$ if $rho$ is sufficiently small. The thermodynamic equilibrium is described by the symmetrised trace of $rm e^-beta Hcal_N$, where $Hcal_N$ denotes the corresponding Hamilton operator. The well-known Feynman-Kac formula reformulates this trace in terms of $N$ interacting Brownian bridges. Due to the symmetrisation, the bridges are organised in an ensemble of cycles of various lengths. The novelty of our approach is a description in terms of a marked Poisson point process whose marks are the cycles. This allows for an asymptotic analysis of the system via a large-deviations analysis of the stationary empirical field. The resulting variational formula ranges over random shift-invariant marked point fields and optimizes the sum of the interaction and the relative entropy with respect to the reference process. In our proof of the lower bound for the free energy, we drop all interaction involving lq infinitely longrq cycles, and their possible presence is signalled by a loss of mass of the lq finitely longrq cycles in the variational formula. In the proof of the upper bound, we only keep the mass on the lq finitely longrq cycles. We expect that the precise relationship between these two bounds lies at the heart of Bose-Einstein condensation and intend to analyse it further in future.
- ItemThe free energy of a box-version of the interacting Bose gas(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2022) Collin, Orphée; Jahnel, Benedikt; König, WolfgangThe interacting quantum Bose gas is a random ensemble of many Brownian bridges (cycles) of various lengths with interactions between any pair of legs of the cycles. It is one of the standard mathematical models in which a proof for the famous Bose--Einstein condensation phase transition is sought for. We introduce a simplified version of the model with an organisation of the particles in deterministic boxes instead of Brownian cycles as the marks of a reference Poisson point process (for simplicity, in Z d, instead of R d). We derive an explicit and interpretable variational formula in the thermodynamic limit for the limiting free energy of the canonical ensemble for any value of the particle density. This formula features all relevant physical quantities of the model, like the microscopic and the macroscopic particle densities, together with their mutual and self-energies and their entropies. The proof method comprises a two-step large-deviation approach for marked Poisson point processes and an explicit distinction into small and large marks. In the characteristic formula, each of the microscopic particles and the statistics of the macroscopic part of the configuration are seen explicitly; the latter receives the interpretation of the condensate. The formula enables us to prove a number of properties of the limiting free energy as a function of the particle density, like differentiability and explicit upper and lower bounds, and a qualitative picture below and above the critical threshold (if it is finite). This proves a modified saturation nature of the phase transition. However, we have not yet succeeded in proving the existence of this phase transition.
- ItemThe longest excursion of a random interacting polymer(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Köcher, Janine; König, WolfgangWe consider a random N-step polymer under the influence of an attractive interaction with the origin and derive a limit law -- after suitable shifting and norming -- for the length of the longest excursion towards the Gumbel distribution. The embodied law of large numbers in particular implies that the longest excursion is of order log N long. The main tools are taken from extreme value theory and renewal theory.
- ItemB12X11(H2)−: exploring the limits of isotopologue selectivity of hydrogen adsorption(London : RSC Publishing, 2021) Wulf, Toshiki; Warneke, Jonas; Heine, ThomasWe study the isotopologue-selective binding of dihydrogen at the undercoordinated boron site of B12X11− (X = H, F, Cl, Br, I, CN) using ab initio quantum chemistry. With a Gibbs free energy of H2 attachment reaching up to 80 kJ mol−1 (ΔG at 300 K for X = CN), these sites are even more attractive than most undercoordinated metal centers studied so far. We thus believe that they can serve as an edge case close to the upper limit of isotopologue-selective H2 adsorption sites. Differences of the zero-point energy of attachment average 5.0 kJ mol−1 between D2 and H2 and 2.7 kJ mol−1 between HD and H2, resulting in hypothetical isotopologue selectivities as high as 2.0 and 1.5, respectively, even at 300 K. Interestingly, even though attachment energies vary substantially according to the chemical nature of X, isotopologue selectivities remain very similar. We find that the H–H activation is so strong that it likely results in the instantaneous heterolytic dissociation of H2 in all cases (except, possibly, for X = H), highlighting the extremely electrophilic nature of B12X11− despite its negative charge. Unfortunately, this high reactivity also makes B12X11− unsuitable for practical application in the field of dihydrogen isotopologue separation. Thus, this example stresses the two-edged nature of strong H2 affinity, yielding a higher isotopologue selectivity on the one hand but risking dissociation on the other, and helps define a window of adsorption energies into which a material for selective adsorption near room temperature should ideally fall.